To find out how much farther Kurt ran than he walked, we need to subtract the distance he walked from the distance he ran.
Kurt ran 9 miles and walked \(\frac{2}{3}\) of a mile.
Now we perform the subtraction:
\[ 9 - \frac{2}{3} \]
To subtract these two numbers, it's helpful to express 9 as a fraction with the same denominator as \(\frac{2}{3}\). The denominator of \(\frac{2}{3}\) is 3, so we can express 9 as:
\[ 9 = \frac{9 \times 3}{1 \times 3} = \frac{27}{3} \]
Now we can subtract:
\[ \frac{27}{3} - \frac{2}{3} = \frac{27 - 2}{3} = \frac{25}{3} \]
Thus, the distance Kurt ran farther than he walked is \(\frac{25}{3}\) miles.
This can also be expressed as a mixed number:
\[ \frac{25}{3} = 8 \frac{1}{3} \]
Therefore, Kurt ran \(\frac{25}{3}\) miles or \(8 \frac{1}{3}\) miles farther than he walked.
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